{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# p18: Chebyshev differentiation via FFT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We repeat p11 but using FFT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "from chebfftPy import chebfft\n",
    "from numpy import pi,linspace,sin,cos,exp,round,zeros,arange,real, flipud\n",
    "from numpy.fft import fft,ifft\n",
    "from matplotlib.pyplot import figure,subplot,plot,grid,title,axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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    "figure(figsize=(10,8))\n",
    "plot_count = 1\n",
    "\n",
    "for N in [10,20]:\n",
    "    xx = linspace(-1.0,1.0,100)\n",
    "    ff = exp(xx)*sin(5*xx)\n",
    "    x = cos(arange(0,N+1)*pi/N)\n",
    "    f = exp(x)*sin(5*x)\n",
    "    error = chebfft(f) - exp(x)*(sin(5*x)+5*cos(5*x))\n",
    "    subplot(3,2,plot_count)\n",
    "    plot_count +=1\n",
    "    plot(xx,ff,'-',x,f,'o')\n",
    "    grid(True)\n",
    "    axis([-1, 1, -4,2])\n",
    "    title('function')\n",
    "    subplot(3,2,plot_count)\n",
    "    plot_count +=1\n",
    "    plot(x,error,'-o')\n",
    "    title('error in derivative')\n",
    "    plot(x,error) \n",
    "    grid(True)"
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